Dynamical system for animal coat pattern model

TL;DR

This paper develops a dynamical system model for animal coat pattern formation based on reaction-diffusion equations, proving mathematical properties and providing numerical illustrations.

Contribution

It introduces a rigorous mathematical framework for the reaction-diffusion model of coat patterns, including existence, uniqueness, and attractor properties.

Findings

Existence and uniqueness of global positive solutions

Continuous dependence on initial conditions

Presence of exponential attractors with estimated fractal dimensions

Abstract

We construct a dynamical system for a reaction diffusion system due to Murray, which relies on the use of the Thomas system nonlinearities and describes the formation of animal coat patterns. First, we prove existence and uniqueness of global positive strong solutions to the system by using semigroup methods. Second, we show that the solutions are continuously dependent on initial values. Third, we show that the dynamical system enjoys exponential attractors whose fractal dimensions can be estimated. Finally, we give a numerical example.